Find the Derivative - d/dx sec(2x)

Problem

d(sec(2*x))/d(x)

Solution

1. Identify the outer function as sec(u) and the inner function as u=2*x

2. Apply the chain rule, which states that (d(ƒ)*(g(x)))/d(x)=ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function sec(u) with respect to u to get sec(u)*tan(u)

4. Differentiate the inner function 2*x with respect to x to get 2

5. Combine the results by multiplying the derivative of the outer function by the derivative of the inner function.

6. Substitute 2*x back in for u

Final Answer

d(sec(2*x))/d(x)=2*sec(2*x)*tan(2*x)

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